Research Interests

My basic interest is in integrable systems. This includes not only dynamical integrable systems, such as geodesic flow on an ellipsoid, the Toda lattice, the Korteweg de Vries equation, and the Nonlinear Schroedinger Equation, but also topics such as orthogonal polynomials and random matrix theory. Within these topics I am particularly interested in asymptotic questions, such as the long-time behavior of solutions of the Korteweg de Vries equation, or the behavior of random matrix ensembles when the size of the matrices becomes large (universality questions). An important tool in my work is the Riemann-Hilbert Problem, and the associated nonlinear steepest-descent method.